The results here enclosed generalize the pionneer work of Lazer and Mac Kenna [1]}, which consider the case where
\(h = c = \alpha = 0\)  and \(F\)  is the Laplacian. In this simple framework, the solutions can be intended in the usual distribution sense, even if the presence of the singular zero order term \(p(x) u^{-\gamma }\)  lead the authors in [1]} to use some tools usually employed in viscosity framework : Existence of convenient sub and super-solutions, comparison Theorem, compactness of bounded sequences. In the present work, the difficulties are linked both to the singularity/degeneracy of the term of higher derivative, and to the singularity of the zero order term.
